V. KLEISNER et al.: IDENTIFICATION AND VERIFICATION OF THE COMPOSITE MATERIAL PARAMETERS ...
IDENTIFICATION AND VERIFICATION OF THE COMPOSITE MATERIAL PARAMETERS FOR THE
LADEVÈZE DAMAGE MODEL
IDENTIFIKACIJA IN VERIFIKACIJA PARAMETROV KOMPOZITNEGA MATERIALA ZA MODEL LADEVÈZE
Václav Kleisner, Robert Zem~ík, Tomá{ Kroupa
University of West Bohemia in Pilsen, Department of Mechanics, Univerzitní 22, 306 14, Plzeò, Czech Republic kleisner@kme.zcu.cz
Prejem rokopisa – received:2011-02-01 ; sprejem za objavo – accepted for publication: 2011-04-14
In this investigation we examine the properties of a layered composite material and verify the Ladevèze material model implemented in PAM-CRASH software. The complex material model incorporates plasticity, failure and damage mechanisms and is suitable for dynamic phenomena, such as crash tests. The experimental tests were performed on appropriate laminated specimens made from unidirectional, pre-impregnated, composite fiber (prepregs) – coupons with axially oriented fibers, coupons with fibers at 45°, and ±45° cross-ply laminates. The tests included simple tensile tests to fracture and cyclic tensile tests. Numerical models were created for the finite-element analysis using shell elements. A mathematical optimization was then used to minimize the error between the experimental and numerical results in terms of load-displacement curves for all the tested configurations by varying the material characteristics.
Keywords: composite, identification, carbon, fiber, epoxy, plasticity, experiment, finite-element analysis
Identifikacija lastnosti plastastega kompozitnega materiala in verifikacja modela Ladeveze za material s PAM-CRASH- sofverom. Kompleksen model materiala vklju~uje plasti~nost, prelom in mehanizem po{kodbe ter je primeren za dinami~ne fenomene kot preizkus trka. Preizkusi so bili izvr{eni na primernih laminatnih vzorcih, izdelanih iz enosmernih predimpregniranih kompozitnih vlaken (prepreg) – kuponov z osno orientiranimi vlakni, kuponov z vlakni pod kotom 45° in kri`nimi laminati ±45°. Preizkusi so obsegali enostavne raztr`ne in cikli~ne natezne preizkuse. Pripravljeni so bili numeri~ni modeli za analizo po metodi kon~nih elementov z uporabo lupinastih elementov. Matemati~na optimizacija je bila nato uporabljena za zmanj{anje napak med eksperimentalnimi in numeri~nimi rezultati s krivuljami obremenitev – pomik za vse preizku{ene konfiguracije s spremembami karakteristik materiala.
Klju~ne besede: kompozit, identifikacija, ogljikova vlakna, epoksi, plasti~nost, preizkusi, kon~na elementna analiza
1 INTRODUCTION
Composite materials are modern materials with advantageous strength- and stiffness-to-mass ratios com- pared to classical materials, such as steel or aluminum1,2. Namely, the carbon-fiber-reinforced plastic composites consisting of continuous carbon fibers and a matrix can have similar or better strength than steel structures and they can have similar or less weight than aluminum structures. As their properties are highly oriented (generally anisotropic), the greatest strength is achieved in the direction of the fibers. This can be utilized especially in the case of the design of components with excessive loading in a specific direction.
Composite materials are increasingly used in the aerospace and automotive industries for the reason mentioned above. Numerical simulations help to design the desired components or complex structures, including the possibility to optimize the fiber orientations or lay-ups. Nevertheless, it is important to know the correct material parameters and to use the appropriate material model. This material data must be obtained from experimental measurements. An integral part of any material model is the failure/damage prediction possi-
bility. Many material models have been proposed so far, but none of them is perfect or universal 6. The basic failure criteria, such as the maximum stress, maximum strain and others, are not interactive criteria. This means that there is no relation between the stress components in different directions. In this respect, the so-called inte- ractive criteria, such as Tsai-Wu1, are more suitable for crash simulations. On the other hand, the disadvantage is that we cannot distinguish between the matrix and fiber failure, which is important in an impact simulation. The most recent failure criteria (the so-called direct mode criteria), such as Puck8or LaRC3, use the advantages of both types9.
The Ladevèze material model 5in the PAM-CRASH software7is implemented only for a multi-layered, thin shell element and transient analysis (i.e., the explicit code). It includes the following modes of failure of a composite material: debonding, micro-cracking, delami- nation, and fiber breaking. The Ladevèze damage model also includes inelastic material deformations caused by the matrix-dominated loading. The plasticity of the matrix cannot be neglected in general and the effect is best seen, for example, in the case of cyclic loading.
Materiali in tehnologije / Materials and technology 45 (2011) 6, 567–570 567
UDK 669.018.9:620.1/.2 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 45(6)567(2011)
2 MATERIAL AND DAMAGE MODELS
The constitutive relationship for materials with a linear response is usually written in the form of the extended Hooke’s law1. The constitutive relationship of the Ladevèze material model can be written with similar formulae, except that elastic constants are herein modified by additional damage parameters or functions
4,5. The crucial relations are summarized inTable 1. The superscript 0 denotes the initial values (damage free) of the material constants. The quantities d11, d22 and d22
represent the fiber damage in tension, matrix damage, and fiber-matrix debonding damage, respectively. The effect of d12 is shown in the relation of the actual (G12) and initial (G012) values of the shear moduli. The shear damage functionY12is derived from the strain energyEd
for an anisotropic material, where YC and Y0 are the critical shear damage limit and the initial shear damage threshold, respectively. The parameter YR represents the shear failure.
Another important improvement to the composite material model is obtained by the inclusion of the matrix plasticity behavior. This is incorporated by changing the yield stress during the cyclic loading. The yield stress is given by R(eP), which is a function of the initial yield stress R0, the plastic deformation eP and the hardening coefficients b,m. This represents a power-law approxi- mation of the experimental curve.
The fiber tensile damage (longitudinal damage) is characterized by the initial (ei11) and ultimate (eu11) fiber tensile damage strains.
3 EXPERIMENT AND SIMULATIONS
In this study, laminated composite coupons made of HexPly 913C prepregs with Tenax HTS 5631 carbon fibers are tested (see Figures 1–3). The material
characteristics needed for the numerical models are obtained from the experimental data. The detailed description of the measurement can be found in 7. It consists of three types of tests:
• simple tensile test on[0]8laminates,
• simple tensile test with load/unload cycles on[±45]2S laminates,
• simple tensile test on[45]8laminates.
Simple[0]tensile test
The tensile test was conducted on UD composite coupons with the [0]8fiber composition (seeFigure 1).
The coupons were loaded by displacement (speed 1 mm/min) until rupture. The force–displacement curve was measured, seeFigure 4.
The initial Young’s modulus E011, the initial fiber failure value ei11 and the critical fiber failure value eu11
were assessed from the data obtained using Hooke’s law.
The averaged experimental results were used directly in the material model within the corresponding numeri- cal simulation. The results of the simulation are in a good
V. KLEISNER et al.: IDENTIFICATION AND VERIFICATION OF THE COMPOSITE MATERIAL PARAMETERS ...
568 Materiali in tehnologije / Materials and technology 45 (2011) 6, 567–570
Tabela 1:Relacije modela Ladevèze za lupinaste elemente4,5 Table 1:Ladevèze model relations for shell elements4,5
Figure 3:Fractured[45]8specimen Slika 3:Prelomljen vzorec[45]8
Figure 2:Fractured[±45]2Sspecimen. The position and orientation of the cracks is emphasized
Slika 2: Prelomljen vzorec [±45]2s. Poudarjena sta polo`aj in orientacija razpok
Figure 1: Fractured[0]8specimen Slika 1:Prelomljen vzorec[0]s
agreement with the experimental data (see Figure 4).
The constants ei11 and eu11 have similar values as the whole cross-section ruptured at the same time.
Cyclic[±45]2Stension test
The composite coupons (Figure 2) were loaded by a cyclic loading – 6 cycles (load/unload) with increasing
load amplitude (700 N, 800 N, 900 N, 1000 N, 1100 N and 1200 N) and the force–displacement curves were obtained. The nonlinear behavior and the plasticity of the composite material can be clearly seen from the results.
This phenomenon is given by the plastic behavior of the matrix or fiber-matrix interface. The stress and strain vectors in the principal material directions (the fiber direction and the transverse fiber direction) must be calculated from the experimental data using the relations for the stress/strain transformation for each lamina.
Consequently, it is possible to calculate the actual shear modulusG12.
The material parameters responsible for the nonlinear response of the numerical model were optimized using the PAM-OPT tool to minimize the error between the simulated and experimental data. Relatively good agreement between the experimental and the simulated curves was obtained; however, the maximum force in this case was not correctly predicted.
Simple[45]8tension test
For the validation of the shear failure parameterYRa simple tension test on the[45]8laminate was performed (Figure 3). This parameter will ensure that the material fails when the load exceeds a certain limitFigure 5.
Recalculation of the cyclic test with the new shear failure parameter in the material model led to a significant improvement of the correlation with the experimental data. The comparison of the resulting curves is shown inFigure 6. The resulting values of all the parameters of the Ladevèze model used are summarized inTable 2.
4 CONCLUSION
The combination of three types of experimental measurements and numerical simulations in the finite-element code PAM-CRASH was performed. A
V. KLEISNER et al.: IDENTIFICATION AND VERIFICATION OF THE COMPOSITE MATERIAL PARAMETERS ...
Materiali in tehnologije / Materials and technology 45 (2011) 6, 567–570 569
Figure 6:Load–displacement curves from[±45]2Stest Slika 6:Krivulji obremenitev – pomik za preizkus[±45]2S
Tabela 2:Identificirane karakteristike materiala Table 2:Identified material characteristics
Figure 5:Load–displacement curves from the[45]8test Slika 5:Krivulji obremenitev – pomik za preizkus[45]8 Figure 4:Load–displacement curves from the[0]8test Slika 4:Krivulji obremenitev – pomik za preizkus[0]8
mathematical optimization was used to obtain the parameters of the used Ladevèze material model that incorporates plasticity, damage and failure. The resulting comparison of the numerical and experimental data in terms of load–displacement curves shows a very good agreement.
In future work, a similar investigation will be performed on textile composites. The applicability of the Ladevèze model will thus be tested on a material with even more complex behavior.
Acknowledgement
The work has been supported by the research project GA CR 101/08/0299 and the research project GA CR 101/08/P091.
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